Optimization of Vehicle Suspensions

OptSusp: Optimization of Vehicle Suspensions is a Matlab package designed to benchmark and optimize passive quarter-car suspensions under standardized stochastic and transient road excitations, combining ISO-based performance metrics with Cross-Entropy global optimization to reveal when asymmetric damping becomes an optimal, scenario-dependent design choice.

OptSusp uses as optimization tool the package CEopt - Cross-Entropy Optimizer, which can be downloaded at https://ceopt.org.

Overview
Features
Usage
Documentation
Authors
Citing OptSusp
License
Institutional support
Funding

Overview

OptSusp was developed to provide a flexible, reproducible MATLAB framework for simulating and optimizing passive vehicle suspension systems, with a particular focus on asymmetric damping, ride comfort, road holding, and transient performance under realistic driving scenarios. The underlying results are reported in the following publication:

J. G. Telles Ribeiro and A. Cunha Jr, Scenario-driven optimization of passive vehicle suspensions: explaining the effectiveness of asymmetric damping, Journal of Vibration Engineering and Technologies, 2026

Preprint available here.

Features

Implements the Cross-Entropy (CE) method for the optimization of passive vehicle suspension parameters
Supports asymmetric damping configurations with independent rebound and compression tuning
Scenario-driven framework combining stochastic road excitation and transient analysis
Simulation-based, gray-box optimization with intuitive and physically meaningful control parameters
Robust to non-convex, non-smooth objective functions arising from nonlinear vehicle dynamics
Modular MATLAB implementation built around a quarter-car model, facilitating extension and reuse
Designed for systematic exploration of comfort–safety–transient trade-offs in suspension design

Usage

To get started with SpringpotTune, follow these steps:

Clone the repository:

git clone https://github.com/americocunhajr/OptSusp.git

Navigate to the code directory:
```
cd OptSusp/OptSusp-1.0
```
To optimize the car suspension, execute the main file:
```
MainCarSuspensionAssymDesign_CE
```

This package includes the following files:

MainCarSuspensionAssymDesign_CE.m - Main script that performs scenario-driven optimization of passive vehicle suspensions with asymmetric damping using the Cross-Entropy method. Defines operating scenarios (road class, speed, vehicle mass), optimization settings, and calls the objective function and dynamic simulations.
MainCarSuspensionDynamics.m - Runs time-domain simulations of the quarter-car model under stochastic (ISO 8608) and deterministic (step and bump) road excitations. Computes sprung-mass acceleration, tire–ground contact force, and transient response metrics.
QuarterCarModel.m - Implements the nonlinear quarter-car model with asymmetric damping and unilateral tire contact.
ObjFunc.m - Defines the scalar objective function used in optimization, combining weighted RMS acceleration, tire–ground contact force variability, and reference targets for scenario-driven trade-off analysis.
isoWdFilter.m - Generates stochastic road profiles based on ISO 8608 spatial power spectral density classes. Converts spatial profiles into time signals according to vehicle speed.
TanhStep.m - Smooth step function based on hyperbolic tangent, used to regularize discontinuities in transient road inputs (step and bump profiles).
dTanhStep.m - Derivative of the smooth step value function, provided for completeness and post-processing consistency.
SoftPlus.m - Numerically stable SoftPlus function used as a smooth approximation of $\max(0,x)$ for regularizing unilateral tire contact and non-smooth nonlinearities.
dSoftPlus.m - Derivative of the stable SoftPlus function, provided for completeness and post-processing consistency.
SmoothAbs.m - Smooth approximation of the absolute value function, used to regularize non-smooth objective-function components.
dSmoothAbs.m - Derivative of the smooth absolute value function, provided for completeness and post-processing consistency.
CEopt.m – Cross-entropy solver

Documentation

The routines in OptSusp are well-commented to explain their functionality. Each routine includes a description of its purpose, inputs, and outputs.

Authors

José Geraldo Telles Ribeiro (UERJ)
Americo Cunha Jr (LNCC / UERJ)

Citing OptSusp

We ask the package users to cite the following manuscript in any publications reporting work done with our code or data:

J. G. Telles Ribeiro and A. Cunha Jr, Scenario-driven optimization of passive vehicle suspensions: explaining the effectiveness of asymmetric damping, Journal of Vibration Engineering and Technologies, 2026

@article{TellesRibeiro2026OptSusp,
   author  = {J. G. {Telles Ribeiro} and A. {Cunha~Jr}},
   title   = "{Scenario-driven optimization of passive vehicle suspensions: explaining the effectiveness of asymmetric damping}",
   journal = {Journal of Vibration Engineering and Technologies},
   year    = {2026},
   volume  = {~},
   pages   = {~},
   doi    = {~},
}

License

OptSusp is released under the MIT license. See the LICENSE file for details. All new contributions must be made under the MIT license.

OptSusp